Proceedings of the ICMC

July 25th-31st, 2021, Santiago, Chile

Contour-Preserving Melody Conversion
Satoru Fukayama and Masataka Goto
National Institute of Advanced Industrial Science and Technology (AIST){s.fukayama, m.goto}@aist.go.jp
ABSTRACTThis paper presents contour-preserving melody conversion
which enables a melody to be brought from one accompaniment to another while preserving the melodic contour.
The conversion automatically adjusts pitches that are inconsistent with the accompaniment and enables convenientinteractive composition. The conversion can be achievedby an optimization using two different probabilistic models: a contour model to preserve the melodic contour, anda consistency model to maintain consistency between the
melody and the accompaniment. The contour model consists of time-varying transition probabilities, and the consistency model is governed by bi-directional recurrent neural networks. For evaluation, we have calculated two measures: the root mean squared difference of intervals tocheck how the conversion preserves the original melodic
contour, and the negative log-probability on test data to
see the consistency between the melody and the accompaniment. The evaluation results indicate that a composer
can control how strictly to preserve the melodic contour bybalancing between the contour model and the consistencymodel.
1. INTRODUCTION
The recent development of fully automatic music generation enables an interactive computer-aided composition
where a composer and an automatic composition collaborate in composing music. Automatic music generation
outputs various musical pieces and inspires the composer
through the iterative uses of automatic music generation. It
can also generate music from speciﬁc fragments of music
such as melodies or chords that are sketched manually by
a composer, and completes or adjusts the remaining partsof the music. Our proposed method contour-preserving
melody conversion is a novel way to compose music interactively with a computer.
Contour-preserving melody conversion regards a melody
by a composer as a source melody and adjusts the pitches
to ﬁt different accompaniments. It enables a composer
to freely explore melodies aside from constraints of theaccompaniment. The overview of our method is shownin Figure 1. To prevent diminishing the character of thesource melody through the conversion, it preserves the
Copyright:©2021 Satoru Fukayama et al.
This is an
open-access article distributed under the terms of theCreative Commons Attribution License 3.0 Unported,which
permits unrestricted use, distribution, and reproduction in any medium,provided the original author and source are credited.

Figure 1. Overview of contour-preserving melody conversion to generate
a novel melody by adjusting pitches in the source melody to ﬁt a different
accompaniment.

melodic contour and the rhythm of the source melody. A
melodic contour is a sequence of single pitches that resembles the original intervallic patterns of a melody, and thecontour can appear with changes in intervallic detail [1].
The experiments show that listeners usually ﬁnd it easy torespond positively to all comparison melodies that share a
melodic contour and respond negatively to melodies withdifferent melodic contours [2, 3].
A technical issue for the contour-preserving melody conversion is to achieve consistency between a melody andthe accompaniment while preserving the original melodic
contour. The accompaniment contains chords, modes, andtonality, and it governs the available pitches in the melody.
The conversion needs to generate a melody which satisﬁes
both the constraints given by a melodic contour and theconsistency between the melody and the accompaniment.
The contribution of this paper is to show that contourpreserving melody conversion can be achieved by solving an optimization problem. The objective function to
maximize consists of two probabilistic models: a contour
model and a consistency model. The contour model comprises a sequence of transition probabilities that represents
the constraints of intervals within a melody. The consistency model is a recurrent neural network (RNN) with longshort-term memory (LSTM) recurrent units [4] that can infer conditional probabilities of pitches when an accompaniment is given. The adjusted pitches for a new melody
are generated by searching for the optimal pitches with dynamic programming.

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2. RELATED WORK
2.1 Generating melody from melodic contour
A system that generates a solo melody from a hand-drawn
curve while satisfying constraints given by a chord sequence in blues style has been proposed [5]. Compared tothis work that allows users to input an abstracted form of
melodic contour to control the results, our work provides
a method to extract it from the existing example, whichenables us to inherit an attractive melodic contour in anexisting melody.
2.2 Generating melodic variations
Our work was inspired by the previous work on generating
variations of a melody [6]. A variation of a melody is probabilistically sampled to have a differentiated rhythm andmelody notes but an impression similar to that of the original melody. Our work shares the philosophy of making
use of melodic structure in existing melodies rather than
generating it from scratch. Using chord sequences to constraint generation of melodic variations has also been proposed [7]. Our work copes with both generating variations
and handling constraints by the accompaniment in a uniﬁed framework.
2.3 Generating sequences with constraints
Our research was also inspired by attempts to create a longterm structure by a Markov chain. A method based on exact sampling with belief propagation to handle dependencies between remote words or melody notes in a sequence
has been proposed [8]. Imposing constraints when sampling from a Markov chain to create long-term repetitive
structures and phrases has also been proposed [9]. Our
method imposes constraints on a probabilistic sequencemodel to generate a melodic contour. However, rather thantrying to generate a structure by learning from data, our approach relies on an existing melody and reuses its melodic
contour to generate a new melody.
2.4 Modeling melody-accompaniment consistency
Our method models the consistency between a melody andan accompaniment. Melody harmonization is the major research theme from this viewpoint. Expert systems [10],neural networks [11, 12], Markov chains [13], hidden
Markov models [14], and log-linear interpolation of probabilistic models [15] have been used. Our method generates
a melody rather than chords, and it could be regarded as adifferent application of modeling the consistency.
2.5 Generating sequence with neural networks
Our work could also be regarded as a melody generation
using neural networks. In recent years, neural networks,
especially Transformers and RNNs have been used forgenerating polyphonic music [16, 17, 18, 19], chord sequences [12], guitar tabs [20], and chorales [21, 19, 22].
DeepBach generates voices of chorales in the style of Johan Sebastian Bach with bi-directional LSTM and Gibbs
sampling [23]. SequenceTutor is a system to adapt RNNs
to generate more preferable melody sequences by applying reinforcement learning [24]. MidiNet and MuseGan

July 25th-31st, 2021, Santiago, Chile
train convolutional neural networks (CNNs) as generative
adversarial networks (GANs) [25, 26]. Counterpoint by
convolution achieves counterpoint with CNNs [27]. Our
method generates a melody by using not only the probability given by the neural networks but also using probabilities from the melodic contour, which provides us withessential constraints to generate melodic variations.
3. CONTOUR-PRESERVING MELODY
CONVERSION
3.1 Composition with contour-preserving melody
conversion
Let us assume that a composer wants to use a melody(the source melody) with a different accompaniment. The
melody initially with an original accompaniment is now
combined with a different accompaniment, and there could
be pitches in a melody that are inconsistent with the
newly attached accompaniment. The preferable method
for computer-aided composition is to automatically adjust
pitches in a melody to be consistent with the new accompaniment. However, the pitches could be changed drastically, and this could change the characteristics of thesource melody.
Our method keeps the original characteristics of the
melody by preserving the melodic contour while adjusting pitches to be consistent with the accompaniment. The
method ﬁrstly creates a contour model from intervals of
the source model. The model comprises a set of transition probabilities to achieve a pitch transition which resembles the intervallic patterns of the source melody. Thenthe method constructs a consistency model by training abi-directional LSTM from paired melody and accompaniment data. Finally, the method executes melody conversion to adjust pitches to meet constrains given by the contour model and the consistency model.
3.2 Contour model
A sequence of intervals can be represented as transition
probabilities between consecutive melody notes. Let us
represent the pitches in a melody as x1 , x2 , . . . , xN , where
xn is the MIDI note number of the nth note and N is thetotal number of notes. A transition probability q(xn |xn−1 )that achieves interval k in semitones between xn−1 and
xn = xn−1 + k is{
1 (xn = xn−1 + k)q(xn |xn−1 ) =(1)0 (otherwise).
Since a melodic contour can appear with changes in intervallic detail, the transition probabilities need to allow thecase when the intervals are slightly different from the original. To achieve this, we design the transition probability
for interval k as:()
1
1
q(xn |xn−1 ) =exp − (xn − (xn−1 + k))2 , (2)
W
2
)
(
∑
1
W =ε+
exp − (xn − (xn−1 + k))2 ,
(3)
2
x
n

where ε is a very small constant for numerical stability.

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July 25th-31st, 2021, Santiago, Chiledimensional one-hot vectors created from the pitches of the
melody notes. Examples of the one-hot vectors are shownon the left in Figure 3. The probability of dropout was set
to 0.3 to avoid overﬁtting, and the step size of the input
was set to K = 10. We used the Adam optimizer [29] tominimize the loss while training with 300 epochs (learning
rate lr = 0.001, β1 = 0.9, β2 = 0.999, ε = 108 ).
3.4 Melody conversion

Figure 2. Network architecture of consistency model which outputs probability for P (xN ) from accompaniment vector inputs
aN −K+1 , aN −K+2 , . . . , aN (step size K).

3.3 Consistency model
We create a consistency model so that we can measure towhat extent the pitches are consistent with the accompaniment. We take a machine learning approach for creating
this model. We chose (1-layer) bi-directional RNNs with
LSTM recurrent units [4] for the neural network structure.
RNNs are used because they can capture the dependencies
between the consecutive melody notes.
An accompaniment behind the melody contains notes
coming from chords and other voices. We denote the probability of having the particular pitch behind the nth melody
note as accompaniment vector an . The dimension of thisvector is the same as the number of available pitches in
MIDI, which is 128. The ith element is deﬁned to be theprobability of having a pitch of MIDI note number i. Examples of the accompaniment vectors are shown on theright in Figure 3. Each value in an accompaniment vector is the ratio of the duration of an accompaniment noteto the duration of a melody note. Suppose we observe a
melody note whose onset time is 0 and the offset time is
100 in MIDI ticks. If we observe an accompaniment consists of single note in pitch 48 where the onset time is 50
and offset time is 200, an accompaniment vector will contain zeros except for the 48-th element, which will be 0.5.
Since the accompaniment note overlaps the melody note at
onset time 50 to offset time 100, the duration of overlapping is 50 whereas the duration of the melody is 100 andthe value for the 48-th element is 0.5 (= (100 − 50)/100).
When an accompaniment has multiple parts or tracks, anaccompaniment vector is ﬁrst created for each accompaniment part. Then the vectors for all parts are combined tocreate a single vector for every melody note by taking the
maximum value among the multiple parts.
The bi-directional RNNs take K accompaniment vectors aN −K+1 , aN −K+2 , . . . , aN as inputs, and they output
probability p(xN ) as a 128 dimensional vector. To achieve
this non-linear transformation from the input to the output, we set the dimension of the hidden units to 32, andset the activation function for input and for the recurrent
input to the rectiﬁed linear unit and sigmoid, respectively.
To ensure the output is a probability distribution, we set asoftmax at the output layer. The network structure of theconsistency model is illustrated in Fig. 2.
We trained the RNNs by minimizing the categorical cross-entropy loss between the output and the 128-

Pitch-contour-preserving melody conversion generates anovel pitch sequence by searching for the optimal pitches
x1 , . . . , xN that maximize the following objective function
J, which combines the contour model and the consistencymodel:
J = ln p(x1 ) +

N
∑

n=2

ln ((1 − λ)p(xn ) + λq(xn |xn−1 )) ,(4)
where λ(0 ≤ λ ≤ 1) is a parameter to balance between
the contour model q(xn |xn−1 ) and the consistency modelp(xn ).
The optimal pitches can be obtained by an efﬁcient(O(N )) algorithm based on dynamic programming. We
show that the maximum value of the objective function J
can be written as a recursive formula and therefore we canuse dynamic programming. Let us denote the maximum
value of J when xn = j by δn (j). We can deriveδn (j) = max J(x1 , . . . , xn−1 , xn = j)
(5)
= max [max J(x1 , . . . , xn−1 = i) + rni,j ](6)i= max [δn−1 (i) + rni,j ],
i

(7)

where
rni,j = ln ((1 − λ)p(xn = j) + λq(xn = j|xn−1 = i))(8)and δn (j) is recursively described by using δn−1 (i). The
resulting algorithm is shown in Alg. 1.
Algorithm 1 Melody conversion
Input: log probabilities ln p(xn ) and rni,jInitialization :1: for j = 1 to 128 do
2:
δ1 (j) = ln p(x1 = j)3:
ψ1 (j) = 0
4: end for
Forward calculation :5: for n = 2 to N do
6:
for j = 1 to 128 do
7:
δn (j) = maxi [δn−1 (i) + rni,j ]8:ψn (j) = argmaxi [δn−1 (i) + rni,j ]9:
end for
10: end for
Backward tracking :11: xN = argmaxj δN (j)12: for n = N − 1 to 1 do
13:
xn = ψn+1 (xn+1 )14: end for
Output: converted pitches x1 , . . . , xN

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July 25th-31st, 2021, Santiago, Chile

Figure 3. Examples of one-hot vectors of pitches in a melody (on the left) and the corresponding accompaniment vectors (on the right) in an excerpt of
RWC-MDB-P-2001 No.97 from the RWC music database [28].

4. MELODY CONVERSION EXPERIMENT
4.1 Balancing between contour and consistency
In order to show contour-preserving melody conversion is
an useful and a feasible method, we conducted an experiment to ﬁnd whether our method can generate melody
pitches that preserve the melodic contour and also maintainthe consistency between the melody and the accompaniment. The possible failures are the two extreme cases. One
is the case that generated pitches preserves the melodic
contour but does not ﬁt the accompaniment. The otherextreme case is when the melodic contour is drasticallychanged by maintaining the consistency given by the consistency model. We investigated the results generated withdifferent choices of parameter λ, which balances between
the contour model and the consistency model in the objective function (eq. (4)).
4.2 Metrics to evaluate contour and consistency
Two quantitative measures were used for evaluation. To
see how a generated melody follows the melodic contourof the source melody, we calculated the root mean squared
difference (RMS) between the intervals of the generated
pitches and the pitches of the source melody. The smaller
the RMS is, the better the generated pitches preserve themelodic contour.
The other evaluation measure was to see how well a generated pitch ﬁts the accompaniment. We used negative logprobability (NLP) calculated by using only the consistencymodel (last term in eq.(4)) divided by the length of the generated pitches. NLP measures how likely it is to observea generated pitch given the trained model with the training data. NLP could be increased by forcing the pitches
to preserve the melodic contour. The smaller the NLP is,
the more likely the generated pitches maintain consistency
with the accompaniment as it is in the training data.
4.3 Melodies used in experiment
We used MIDI ﬁles of popular music (RWC-MDB-P-2001
No. 1-30) from the RWC Music Database [28]. Vocal
tracks containing melodies were manually detected. The
remaining tracks except for drums were collected to prepare accompaniment vectors.
We trained parameters of RNNs by using all melody
notes in RWC-MDB-P-2001 No. 1-20 (training data). To

Figure 4. Pitches generating when converting pitches of RWC-MDB-P2001 No. 27 to ﬁt the accompaniment of RWC-MDB-P-2001 No. 26 with
six different λ. The melodic contour follows that of the source melody(baseline) when λ is close to 1.0.

test the contour-preserved melody conversion, we used 8bars from the beginning of verse A of RWC-MDB-P-2001
No. 21-30 (test data). For all combinations of 10 songs(90 = 10 × (10 − 1) possibilities excluding the conversion
using the original accompaniment), one song was used forthe melodic contour, and the other was used for the accompaniment.
The evaluation metrics RMS and NLP were calculated forevery combination of songs, and statistics of the metrics(mean and standard deviation) were calculated. We tried 6
different settings for λ = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0.
4.4 Melody conversion results
The results obtained when converting pitches of RWCMDB-P-2001 No. 27 to ﬁt the accompaniment of RWCMDB-P-2001 No. 26 are shown in Figure 4. We observedthat the melodic contour gradually followed the original
melodic contour of the source melody more and moreclosely as λ was gradually increased from 0.0 to 1.0.
Mean and standard deviation of evaluation metrics (RMS
and NLP) calculated when varying λ are shown in Figure 5. By setting λ around 0.4, the method generated
pitches preserving the original contour within 3 semitonesof difference (RMS: 2.46 ± 1.18, NLP: 2.00 ± 0.733). The
extreme case of ignoring the melodic contour appeared
when we set λ to 0.0 resulting in around 5 semitones dif-

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Figure 5. Mean and standard deviation of evaluation metrics (RMS and
NLP) by varying λ to balance between preserving the melodic contour
and maintaining the consistency between the melody and the accompaniment.

proposed (λ=0.0)
proposed (λ=0.4)
proposed (λ=1.0)
source melody
human

NLP
0.454 ± 0.113
2.00 ± 0.733
7.13 ± 2.74
9.36 ± 3.58
7.01 ± 2.01

Table 1. Comparison of negative log-probability among proposed method(proposed), using the pitches of the source melody (source melody), andthe human-composed melodies with the accompaniment (human).

ference (RMS: 4.54 ± 1.31). The other extreme case ofignoring the accompaniment was obtained by setting λ to1.0, for which the NLP was the highest among all settingsof λ (NLP: 7.13±2.72). This highest NLP value was lower
than the baseline result (NLP: 9.36 ± 3.58), which reuses
the original pitches in the source melody.
5. DISCUSSION
We have found that contour-preserving melody conversion
generates novel pitches based on an existing melodic contour. The experimental results indicate that a composer
can balance between strictly preserving the melodic contour and maintaining consistency of melody and the accompaniment by setting λ.
There are issues we would like to deal with in future
work. The ﬁrst issue is the phrase boundaries within a
melody. We discarded the length of melody notes andequally handled all intervals between consecutive notes. It
seems more valuable not to preserve the interval between
phrases that are separated far apart. The constraints of
melodic contour between phrases could be relaxed by locally increasing λ for creating transition probabilities depending on the onset-to-onset duration of notes.
Rhythm is another important melodic structure we would
like to consider. In order not to copy the rhythm but toinherit the rhythm structure, we need an abstracted form of
rhythm. This could be done by estimating a tree structure
behind the observed rhythm and using the tree to adapt toan arbitrary number of melody notes but still preserve thecharacter of the rhythm.
The third issue is the listening test. While the NLP indicates how likely the generated pitches maintain consis-

July 25th-31st, 2021, Santiago, Chiletency with the accompaniment, it depends on how well theconsistency model is trained. The comparison of the negative log-probability of the generated pitches is shown in
Table 1. The value for the proposed method at λ = 0.4 islower than that for the human-composed melodies (2.00 <7.01). Since the NLP values for the training and validation
data were signiﬁcantly lower (0.877 ± 0.398), the consistency model seemed to constrain too much on the pitches.
This should be conﬁrmed through listening test to obtainsubjective evaluation.
Although using a stronger and better-trained consistencymodel is our future work, our contour-preserving melody
conversion is useful for interactive computer-aided composition applications. The parameter λ provides a ﬂexible control between the fully automatic composition andthe manual composition. A composer can explore various possibilities of melodies, from the most recommended
ones to the one strictly preserving the melodic contour ofcomposer’s manual composition.
6. CONCLUSION
We discussed contour-preserving melody conversion for
the interactive computer-aided composition of melodies.
We formalized the conversion as an optimization problem to maximize the log-probability of pitches with analgorithm based on dynamic programming. The experimental results indicated that composers could obtain various melodies by balancing between strictly preserving the
melodic contour and maintaining the consistency between
the melody and the accompaniment. In the future, wewould like to generalize this approach to handle chords,
rhythms, and musical structures.
Acknowledgments
This work was supported in part by JST ACCEL Grant
Number JPMJAC1602, Japan. We thank Yi-Hsuan Yang
(Academia Sinica) for his valuable comments.
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